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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
1.2K
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

2.2K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

58.5K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
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Related Experiment Video

Updated: Dec 28, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Multistability of Driven-Dissipative Quantum Spins.

Haggai Landa1, Marco Schiró2, Grégoire Misguich1,3

  • 1Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, 91191 Gif-sur-Yvette, France.

Physical Review Letters
|February 15, 2020
PubMed
Summary

Quantum spin dynamics reveal that correlations eliminate multistability in 1D lattices. In 2D and higher, multistability persists in the thermodynamic limit, with parameter variations causing jumps between steady states.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Many-body dynamics

Background:

  • Lattice models of quantum spins (spin-1/2) are studied under coherent drive and dissipation.
  • Mean-field theory often predicts multistable parameter regions with coexisting steady states.

Purpose of the Study:

  • To develop an efficient scheme for corrections to mean-field theory using correlations.
  • To investigate the impact of correlations on the steady states of quantum spin models.
  • To explore the dimensionality dependence of multistability in driven-dissipative quantum systems.

Main Methods:

  • Development of a leading-order correlation-corrected scheme.
  • High-precision numerical benchmarking using matrix-product operators (MPOs).
  • Analysis of one- and two-dimensional lattice models.

Main Results:

  • Correlations eliminate mean-field bistability in 1D, leading to a unique steady state.
  • Multistability is possible in 2D and higher dimensions when the thermodynamic limit is taken first.
  • Parameter variations induce jumps between steady states, exhibiting critical slowing down.

Conclusions:

  • Correlations play a crucial role in determining the steady-state properties of quantum spin models.
  • Dimensionality and the order of limits (thermodynamic vs. long-time) are critical for multistability.
  • Trapped-ion experiments offer a platform to explore these nonequilibrium phenomena beyond current numerical capabilities.